Age-related changes in anatomical and morphological leaf traits of Wollemia nobilis

The results highlight significant variations of Wollemia nobilis leaf traits which reflect age-related changes of the subsequent growth units along the branches. Age-related changes appear in a gradual increase of leaf size from young leaves to old leaves. The LMA increasing from 13.75 g/cm(2) in current year leaves to 24.84 g/cm(2) in 7 year leaves is associated with an increment of the number of lignified elements (vascular tissues, astrosclereids), of hypodermal and epidermal-cuticle structures (cuticle, wax layer) and of oil bodies abundance, which may increase resistance to stress factors. These characteristics highlight that W. nobilis leaves can adapt to variable environmental conditions with a return rate on a larger time-scale since leaves on a branch stay alive for a long time until the branch dies

Landscape statistics of the low autocorrelated binary string problem

The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing literature, namely, depth and difficulty, we find that the landscape of LABSP, except perhaps for a very large degeneracy of the local minima energies, is qualitatively similar to some well-known landscapes such as that of the mean-field 2-spin glass model. Furthermore, we consider a mean-field approximation to the pure model proposed by Bouchaud and Mezard (1994, J. Physique I France 4 1109) and show both analytically and numerically that it describes extremely well the statistical properties of LABSP

Last passage percolation and traveling fronts

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped and move like a traveling wave, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. The Gumbel distribution plays a central role for the particle jumps, and we show that the scaling limit is a L\'evy process in this case. The case of bounded jumps yields a completely different behavior

Phase transition and landscape statistics of the number partitioning problem

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution, is investigated by examining the energy landscape of this classic optimization problem. This is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure, termed a barrier tree, the leaves and internal nodes of which represent, respectively, the minima and the lowest energy saddles connecting those minima. Here we apply several measures of shape (balance and symmetry) as well as of branch lengths (barrier heights) to the barrier trees that result from the landscape of the NPP, aiming at identifying traces of the easy/hard transition. We find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights. Only the {\it difficulty} measure, given by the maximum value of the ratio between the barrier height and the energy surplus of local minima, succeeded in detecting traces of the phase transition in the tree. In adddition, we show that the barrier trees associated with the NPP are very similar to random trees, contrasting dramatically with trees associated with the $p$ spin-glass and random energy models. We also examine critically a recent conjecture on the equivalence between the NPP and a truncated random energy model

Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities

The Princeton Protein Orthology Database (P-POD): A Comparative Genomics Analysis Tool for Biologists

Many biological databases that provide comparative genomics information and tools are now available on the internet. While certainly quite useful, to our knowledge none of the existing databases combine results from multiple comparative genomics methods with manually curated information from the literature. Here we describe the Princeton Protein Orthology Database (P-POD, http://ortholog.princeton.edu), a user-friendly database system that allows users to find and visualize the phylogenetic relationships among predicted orthologs (based on the OrthoMCL method) to a query gene from any of eight eukaryotic organisms, and to see the orthologs in a wider evolutionary context (based on the Jaccard clustering method). In addition to the phylogenetic information, the database contains experimental results manually collected from the literature that can be compared to the computational analyses, as well as links to relevant human disease and gene information via the OMIM, model organism, and sequence databases. Our aim is for the P-POD resource to be extremely useful to typical experimental biologists wanting to learn more about the evolutionary context of their favorite genes. P-POD is based on the commonly used Generic Model Organism Database (GMOD) schema and can be downloaded in its entirety for installation on one's own system. Thus, bioinformaticians and software developers may also find P-POD useful because they can use the P-POD database infrastructure when developing their own comparative genomics resources and database tools